Capacitors can be made by attaching metal layers onto opposing surfaces of a dielectric material. The physical and geometric properties of the dielectric material determine the capacitance and other properties of the capacitor. In many applications, it is desired for a capacitor to have a high energy density and low dissipation. Capacitors using polymer film for the dielectric material have certain advantages over ceramic-based capacitors, such as improved high-temperature characteristics, low dissipation factors, and improved tolerance to mechanical stress. However, polymer film capacitors have typically not been able to achieve energy densities much higher than about 1 J/cc. Accordingly, a need exists for an improved polymer film capacitor.